Limit theorems for stochastic Volterra processes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910240153272320 |
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| author | Bianchi, Luigi Amedeo Bonaccorsi, Stefano Cañadas, Ole Friesen, Martin |
| author_facet | Bianchi, Luigi Amedeo Bonaccorsi, Stefano Cañadas, Ole Friesen, Martin |
| contents | We introduce an abstract Hilbert space-valued framework of Markovian lifts for stochastic Volterra equations with operator-valued Volterra kernels. Our main results address the existence and characterisation of possibly multiple limit distributions and stationary processes, a law of large numbers including a convergence rate, and the central limit theorem for time averages of the process within the Gaussian domain of attraction. As particular examples, we study Markovian lifts based on Laplace transforms in a weighted Hilbert space of densities and Markovian lifts based on the shift semigroup on the Filipović space. We illustrate our results for the case of fractional stochastic Volterra equations with additive or multiplicative Gaussian noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08466 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit theorems for stochastic Volterra processes Bianchi, Luigi Amedeo Bonaccorsi, Stefano Cañadas, Ole Friesen, Martin Probability 60G22, 45D05, 60H15, 60G10, 60B10, 60F25, 60F05 We introduce an abstract Hilbert space-valued framework of Markovian lifts for stochastic Volterra equations with operator-valued Volterra kernels. Our main results address the existence and characterisation of possibly multiple limit distributions and stationary processes, a law of large numbers including a convergence rate, and the central limit theorem for time averages of the process within the Gaussian domain of attraction. As particular examples, we study Markovian lifts based on Laplace transforms in a weighted Hilbert space of densities and Markovian lifts based on the shift semigroup on the Filipović space. We illustrate our results for the case of fractional stochastic Volterra equations with additive or multiplicative Gaussian noise. |
| title | Limit theorems for stochastic Volterra processes |
| topic | Probability 60G22, 45D05, 60H15, 60G10, 60B10, 60F25, 60F05 |
| url | https://arxiv.org/abs/2509.08466 |